Potential energy and work

Here, the usual unit for AH and Q is the (Btu), whereas kinetic energy, potential energy, and work are usually expressed as (f lbf). Therefore the factor 778.16(ftlbf)(Btu) l must be used with the appropriate terms to put them all in consistent units of either (ft lbf) or (Btu). 

List and apply the equations used to calculate kinetic energy, potential energy, and work. 

Figure 4.36. Effect of catalyst potential UWR and work function on the activation energy E (squares) and preexponential factor r° (circles) of C2H4 oxidation on Rh/YSZ. open symbols open-circuit conditions. Te is the isokinetic temperature 372°C and r is the open-circuit preexponential factor. Conditions po2=l.3 kPa, pc2n =7.4 kPa.50 Reprinted with permission from Academic Press.

Figure 8.24. Effect of catalyst potential Uwr and work function change (vs 1=0) on the activation energy E and preexponential factor K° of the kinetic constant K of CH4 oxidation to C02 an average T value of 948 K is used in the rhs ordinate p°H4 =p°2 =2kPa, 29Reprinted with permission from Academic Press.

Consider the case of a junction between two different metals a and p. Generally, they will have different values of the Fermi energy and work function. Between the two metals, a certain Volta potential will be set up. This implies that the outer potentials at points a and b, which are just outside the two metals, are different. However, it will be preferable to count the Fermi levels or electrochemical potentials from a common point of reference. This can be either point a or point b. Since these two points are located in the same phase, the potential difference between them (the Vofta potential) can be measured. Hence, values counted from one of the points of reference are readily converted to the other point of reference when required. 

If a flow reaction proceeds with negligible changes in kinetic energy and potential energy and involves no form of work beyond that required for the flow, the heat added is equal to the increase of enthalpy of the system... 

Looking at a little slice of the process fluid as our system, we can derive each of the terms of Eq. (2.18). Potential-energy and kinetic-energy terms are assumed negligible, and there is no work term. The simplified forms of the internal ener and enthalpy are assumed. Diffusive flow is assumed negligible compared to bulk flow. We will include the possibility for conduction of heat axially along the reactor due to molecular or turbulent conduction. 

The energy Ei is the sum of the internal energy, the kinetic energy, the potential energy, and other energies in the i-component. In a CSTR, the value of Ei is equal to the internal energy. Also, in a CSTR, the work term W is reduced to the flow work and can be written as ... 

In this work, the electronic kinetic energy is expressed in terms of the potential energy and derivatives of the potential energy with respect to nuclear coordinates, by use of the virial theorem (5-5). Thus, the results are valid for ail bound electronic states. However, the functional derived for E does not obey a variational principle with respect to (Pg ( )), even though in... 

A plot of wfPp(z) for rs = 3.24 employing the orbitals of the finite-linear-potential moder is given in Fig. 6. The corresponding local density approximation (LDA) potential is also plotted. In the interior and about the surface of the metal the two potentials are equivalent. But outside the surface vxapp(z) improves upon the LDA significantly and approaches the exact structure asymptotically. We thus expect that properties such as the surface energy and work function obtained with Eapp[p] and v pp(r) to be superior to those of the LDA. Such self-consistent calculations are in progress. 

By Eq. (2.30), neglecting kinetic and potential energies and setting the heat and work terms equal to zero ... 

Solution Row through a partly closed valve is known as a throttling process. Since flow is at a steady rate, Eq. (2.10) applies. The line is insulated, making Q small moreover, the potential-energy and kinetic-energy changes are negligible. Since no shaft work is accomplished, Ws = 0. Hence, Eq. (2.10) reduces to... 

The second term in the mechanical-energy balance. Equation 5.1, is the change in potential energy and requires no comment. The third term is "pressme work" and its evaluation depends on whether the fluid is compressible or incompressible. Because the increase in pressure across the fan is small, we treat the flow as essentially incompressible. Thus, the fluid density may be removed from the integral sign and the mechanical energy balance becomes... 

To obtain an equation for calculating the work of conpression, first apply Bernoulli s equation, Equation 5.1, across the compressor. The first term, the kinetic energy term, is small compared to the other terms in the balance. The second term is the change in potential energy, and it is also small. The last two terms are the work done by the system and the friction loss. First, we consider frictionless flow. Thus, the compressor work. 

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